Virus vs worm

What exactly is the difference between a virus and a worm? Bruce Davie in his 6.829 class last week said security was one of those things that you truly dont know unless you know all of it. He also said it was difficult for him to get a clear definition for virus and worm. The final one he settled on, was that a virus, like a biological virus, does not actually have the code for replication and requires a host. Whereas, a worm has a life of its own, i.e. it has the code to replicate itself. No user action is required to replicate a worm.